Cute Loot

A Chubby is not a specific enemy, it's just a very rare "fat" version of one of the following enemies: Varkid, Spiderant, Skag, Stalker, Midget, Rakk.The best place to find a Chubby Varkid is in the starting area of the Caustic Caverns. It has a fixed spawn point where the first group (of Varkids) is located, right next to the fast travel station. You can back out to the main menu and hit continue to make all enemies respawn.

Playing co-op greatly increases the chances of finding a Chubby enemy! With a group of 4 people you will stumble across such a Chubby very soon. In single player it can take hours or days. The Caustic Caverns also have other areas where Chubby Varkids and Chubby Spiderants can spawn. Just roam around this area with a bunch of friends in co-op mode to find them more quickly. Only the person who kills the Chubby will get the trophy / achievement.